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It’s not as if the Indiana state legislature didn’t do due diligence before attempting to define the value of pi. The House sent the bill first to the Committee on Swamp Lands. When they approved it, the Senate referred it to the Committee on Temperance, who also said it seemed OK to them. That’s more consideration and expert attention than many bills get.

just for giggles i made an a spreadsheet that does 60k iterations of that formula. At 60,000 the number for pi is 3.141609321. so to even get the first 10 or so digits correct, it’s gonna take ~1 million iterations I would guess? Sure wouldn’t want to do that by hand :)

Limited precision arithmetic can make a series converge to a wrong value. I once wrote a program that failed similarly, and I eventually figured out that, beyond a certain n, some critical operand was rounding down to 0 in the middle of the iteration.

Spreadsheets aren’t good for accurate floating point calculations. http://blogs.office.com/b/microsoft-excel/archive/2008/04/10/understanding-floating-point-precision-aka-why-does-excel-give-me-seemingly-wrong-answers.aspx

If you ever do get the urge for “hands-on pi,” here’s a kinda neat method to hone in on pi’s value (no circles or tricky math required):

You need a bunch of toothpicks, and a wood floor whose slats are as wide as the toothpicks are long. Hold a toothpick at chest level, then drop it onto the floor. Once the toothpick is at rest, record whether or not it crosses a gap between floorboards. Repeat…. The ratio of non-crossings to crossings will approximate pi.

The bit of the Bible in question is in the first book of Kings and describes a vessel in the Temple of Solomon…

He made the [vessel] of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it.

If you do the maths on that, Pi equals 3. Derp.

The explanation put forward by people who can’t countenance the idea that the holy-sacred-literal-unalterable-word-of-almighty-god could contain a rough estimate (which is, frankly the most likely explanation) is that the vessel was irregular in shape and flared out a bit at the top. That way the maths works out fine.

Or just that the vessel had non-zero thickness, and “rim to rim” was measuring the vessel’s capacity, and “measure around it” was giving the outer dimension.[edit: this was posted below, and yeah, me wrong.]

Cubits are normally measured with your arm. They may have measured the 30 cubits around using a line, at whatever level of precision they got, but the “10 cubits from rim to rim” is highly unlikely to have been precise enough to distinguish it from 9.5 cubits.

I heard someone explain the pi=3 bible thing as when you measure across you are taking an interior measurement but when you measure around you are taking an external measurement so the thickness of the vessel makes the bible description possible to be correct without making pi=3

Except that 30 cubits (implying pi=3) is less than the 31.415… cubits it should be. Measuring the circumference around the external measurement when the diameter is measured internally would give you a ratio even bigger than pi, not less.

In First Kings, Hiram made a big bowl. How big was it? Ten cubits across. Thirty cubits around. Pretty big for a bowl. That was the point.

I can’t even claim this is a cheap shot. There are Christians who would argue that pi must be 30 / 10 because the Bible says so. As someone who takes the Bible seriously, I get really embarrassed when (a few of) my co-religionists try to tease out God’s hidden scientific truths in the Scripture.

A result of circumference 30 and diameter 10 is consistent with pi when you consider that they are just rounding to the nearest unit. Did their number system even have a way of representing complicated fractions?

For example 9.65 cubits and 30.32 cubits might be the actual measurements that agree with a true value of pi but rounded off they would give 10 and 30.

Do we suppose that anyone seeing this structure had a cubit tape measure accurate to 100ths? More likely they made a quick measure so they could describe the size of it.

It isn’t as if the writer of that passage is making a huge error. The error is not recognizing how the writer was using numbers.